The linear theory of functional differential equations: existence theorems and the problem of pointwise completeness of the solutions

Journal Article · Thu Mar 31 00:00:00 EDT 2011 · Sbornik. Mathematics

DOI:https://doi.org/10.1070/SM2011V202N03ABEH004147; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)· OSTI ID:21592557

Beklaryan, Leva A ^[1]

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1. Central Economics and Mathematics Institute, RAS, Moscow (Russian Federation)

A boundary value problem and an initial-boundary value problems are considered for a linear functional differential equation of point type. A suitable scale of functional spaces is introduced and existence theorems for solutions are stated in terms of this scale, in a form analogous to Noether's theorem. A key fact is established for the initial boundary value problem: the space of classical solutions of the adjoint equation must be extended to include impulsive solutions. A test for the pointwise completeness of solutions is obtained. The results presented are based on a formalism developed by the author for this type of equation. Bibliography: 7 titles.

• OSTI ID: 21592557
• Journal Information: Sbornik. Mathematics, Vol. 202, Issue 3; Other Information: DOI: 10.1070/SM2011v202n03ABEH004147; Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
ALGORITHMS
BOUNDARY-VALUE PROBLEMS
DIFFERENTIAL EQUATIONS
MATHEMATICAL SOLUTIONS
MATHEMATICAL SPACE
EQUATIONS
MATHEMATICAL LOGIC
SPACE